Before: structurally sound but plenty of surface rust inside the tank:
Four litres of full-fat Coke (it's interesting that now the sugar tax is in, 2 litres of classic Coke is about £1.60, more expensive than Diet Coke, but Sainsbury's own sugar coke is 38p for two litres - it's a brand tax, not a sugar tax...) and a pint's worth of sharp gravel.
Slosh this round and round and up and down etc to knock off all the rust flakes. Leave for a while, repeat a few times and then drain the tank of coke and gravel (lots more upside-down shaking required), and then flush out with water.
Next, dilute a litre of Caswell's Rust Remover (other products are available) as per the directions and fill the tank to the top.
Leave for 6 hours and then poke around inside with a long bent brush thing as much as you can, and then drain. The rust remover uses 'the power of lemons' which is presumably citric acid, and is safe to dispose of down the drain (although it will bleach your shirt if you splash it).
Flush the tank thoroughly from the hosepipe, and then use a hot-air paint stripper gently on the outside and through the filler hole to dry it thoroughly so that surface rust doesn't reappear.
And the job's done.